A traveling-wave tube has been conventionally used as a power amplifier for microwave frequency signals. Recently, the use of MESFETs (metal semiconductor FETs) using a compound semiconductor, GaAs, in place of such traveling-wave tubes is attracting attention. However, in order to use MESFETs in place of traveling-wave tubes, it is necessary to improve the power and gain characteristics of MESFET's. An example of MESFET's is shown in FIG. 1. The MESFET shown in FIG. 1 comprises a semi-insulating GaAs substrate 1 and an active GaAs layer 2 on the substrate 1. The active GaAs layer 2 is doped with an N-type impurity. On the active layer 2, a drain electrode 3 and a source electrode 4 are disposed spaced from each other. A recess 5 is formed in the active layer 2 in the space between the drain and source electrodes. A metallic gate electrode 6 is disposed in the recess 5.
The maximum power of this MESFET is determined by the product of its maximum channel current If and its breakdown withstanding voltage VB (i.e. the maximum reverse voltage which can be applied between the gate electrode 6 and the drain electrode 3). According to an article "Channel Current Limitations in GaAs MESFETS" by Hatsuaki Fukui in Solid-State Electronics, Vol. 22, Pages 507-515, If can be expressed as: EQU If=q.multidot.Vs.multidot.Nd.multidot.Z.multidot.a(1-Pm) (1).
In this equation (1), q is the unit charge, Vs is a saturation velocity, Nd is a doping concentration which is the quantity of charge per unit volume, Z is the width of the gate, a is the thickness of the GaAs layer 2 immediately beneath the gate electrode 6 (as indicated in FIG. 1), and Pm is the channel openability at the minimum reduced potential at the drain-side end of the gate. As is understood from the above equation (1), If is proportional to the product of the thickness a of the active layer 2, the doping concentration Nd in the layer 2 and the carrier saturation velocity Vs in the layer 2. On the other hand, according to an article "Power-Limiting Breakdown Effects in GaAs MESFET's" by William R. Frensley in IEEE TRANSACTIONS ON ELECTRON DEVICES, Vol. ED-28 No. 8, August 1981, Pages 962-970, VB is inversely proportional to the product of Nd and a, i.e. the amount of charge per unit area. Accordingly, it is possible to increase the maximum channel current If by increasing the saturation velocity Vs, without increasing the product of Nd by a, i.e. without reducing the breakdown withstanding voltage VB.
In order to increase the gain, it is necessary to increase the cutoff frequency f.sub.T. It is known that the cutoff frequency f.sub.T is proportional to the saturation velocity Vs and inversely proportional to the gate length L. At the cutoff frequency f.sub.T, which is the frequency at which the current amplification factor is unity (1), the current flowing through the gate-source capacitance C.sub.gs is expressed as .omega..sub.T C.sub.gs Vi, where Vi is the gate-source voltage, and .omega..sub.T is 2.pi.f.sub.T. This current is equal to the current gmVi which flows in the drain, where gm is the transconductance. Then, the cutoff frequency f.sub.T is expressed as: EQU f.sub.T =gm/2.pi.C.sub.gs
where gm is .epsilon.ZVs/W. .epsilon. is the dielectric constant of the active layer 2, Z is the gate width, and W is the thickness of the depletion region in the active layer 2. More specifically, gm is defined as .delta.Id/.delta.Vg at a drain voltage Vd held constant, where Id is a drain current, Vg is a gate voltage. From equation (1), the drain current Id is expressed as: EQU Id=q.multidot.Nd.multidot.Vs.multidot.Z(a-a.multidot.Pm) (2).
In the equation (2), a.multidot.Pm represents the thickness of the active layer 2. It is known that the thickness W of the depletion region in the active layer 2 can be expressed as: ##EQU1## where Vb is an internal potential. From the equations (2) and (3), gm can be expressed as: ##EQU2## C.sub.gs can be expressed as .epsilon.LZ/W. Accordingly, the cutoff frequency f.sub.T can be expressed, by substituting gm as expressed by the equation (4) and .epsilon.LZ/W for gm and C.sub.gs, respectively, in the equation f.sub.T =gm/2.pi.C.sub.gs, as Vs/2.pi.L. This expression indicates that the cutoff frequency f.sub.T is proportional to the saturation velocity Vs and is inversely proportional to the gate length L.
Therefore, it is understood that increasing the saturation velocity Vs for the required product Nd.a for a desired VB is an efficient way to increase both the power and gain of an MESFET. For applications in which a high saturation velocity Vs is desired, an HEMT as shown in FIG. 2 may be advantageously used. The HEMT of FIG. 2 comprises a semi-insulating GaAs substrate 7, an undoped GaAs channel layer 8 on the substrate 7, and a heavily doped N-type Al.sub.x Ga.sub.1-x As electron supply layer 9 on the undoped GaAs channel layer 8. A recess 10, a gate electrode 11, a drain electrode 12, and a source electrode 13 similar to those of an MESFET are also included. The channel layer 8 has larger electron affinity than the electron supply layer 9 so that a heterojunction is formed between the electron supply layer 9 and the channel layer 8, and, accordingly, a two-dimensional electron gas layer 14 with a large saturation velocity is formed at the junction between the channel layer 8 and the electron supply layer 9.
In an HEMT, the maximum number of two-dimensional carriers per unit area, Ns, i.e., the maximum quantity of charge per unit area in a heterojunction, can be expressed as: EQU Ns=[2.epsilon.N(.DELTA.Ec-Ef)/q].sup.1/2 ( 5)
where .epsilon. is the dielectric constant of the channel layer 8, N is the free electron concentration of the N-type Al.sub.x Ga.sub.1-x As electron supply layer 9, .DELTA.Ec is the difference between the conduction band energies of the channel layer 8 and the electron supply layer 9 at the interface therebetween, Ef is the Fermi level, and q is the quantity of electrical charge. Frequently, x=0.3 is used for the electron supply layer 9 with silicon being used as an impurity. That is, Si-doped N-type Al.sub.0.3 Ga.sub.0.7 As is frequently used for the electron supply layer 9. In this case, the concentration of free electrons N does not monotonically increase with the Si doping level. This is because in Si-doped N-type Al.sub.0.3 Ga.sub.0.7 As, a deep level called a DX center is formed. The upper limit of N is about 1.times.10.sup.18 cm.sup.-3. Substitution of N.perspectiveto.1.times.10.sup.18 cm.sup.-3, .epsilon.=8.85.times.10.sup.-14 .times.12.5, .DELTA.Ec=0.2244 eV, Ef.perspectiveto.0.1 eV, and q=1.6.times.10.sup.-19 in equation (5), indicates that the maximum number of two-dimensional carriers Ns is about 1.times.10.sup.12 cm.sup.-2. The value for .DELTA.Ec has been calculated by assuming that the energy gaps of Al.sub.0.3 Ga.sub.0.7 As and GaAs are 1.798 eV and 1.424 eV, and multiplying the difference by 0.6. With the quantity of charge per unit area, Ns, being used in place of the quantity of charge per unit volume, Nd.multidot.a, in equation (1), the maximum channel current If for the HEMT can be expressed as follows. It should be noted that because of the HEMT, no depletion region is formed in the two-dimensional electron gas layer 14 and, therefore, the term a.multidot.Pm is removed. EQU If=q.multidot.Vs.multidot.Ns.multidot.Z (6).
Substituting 1.6.times.10.sup.-19 (C), 2.times.10.sup.7 (cm/second), 1.times.10.sup.12 (cm.sup.-2), and 0.1 (cm) for q, Vs, Z, respectively, in equation (6), it is seen that If is 0.32 A/mm. It is known that in order to provide a breakdown withstanding voltage VB of 25 V or higher for a GaAs MESFET having a gate recess with steps, the product Nd.multidot.a should be 2.4.times.10.sup.12 charge/cm.sup.2. In this case, assuming that Z=0.1 cm, If calculated from equation (1) is 400 mA/mm. Thus, it is seen that If for HEMTs is smaller than If for MESFETs.
The breakdown withstanding voltage VB of HEMTs is also inversely proportional to the product of the quantity of electrical charge per unit area or doping concentration Nd and the thickness a of the electron supply layer 9. Accordingly, in order to obtain the maximum number of two-dimensional carriers per unit area, i.e., an Ns of about 1.times.10.sup.18 cm.sup.-2, the doping concentration of silicon must be 4.times.10.sup.18 cm.sup.-3 and the thickness a must be 350 .ANG.. In other words, the free electron concentration N for Ns of about 1.times.10.sup.12 cm.sup.-2 can be calculated by substituting the above-quoted values for q, .epsilon., Ns, .DELTA.Ec, and Ef in the equation N=q.multidot.Ns.sup.2 /2.epsilon.(.DELTA.Ec-Ef), which is derived from equation (5). From the calculation it is seen that the required N is 5.83.times.10.sup.17 cm.sup.-3. Since a deep level is formed, the free electron concentration N of N-type Al.sub.x Ga.sub.1-x As is about 10-20% of the silicon doping level when x is equal to 0.3. Accordingly, for obtaining a free electron concentration N of, for example, 15% of the silicon doping level, the silicon doping concentration Nd should be 5.83.times.10.sup.17 /0.15.perspectiveto.4.times.10.sup. 18 cm.sup.-3.
The number of two-dimensional carriers per unit area, Ns, is determined by the product of the thickness d of the electron supply layer 9, which supplies two dimensional carriers, by the free electron concentration N. Thus, the thickness d should be Ns/N=1.times.10.sup.12 /5.83.times.10.sup.17 .perspectiveto.172 .ANG.. Since the gate electrode 11 is a metallic electrode, a depletion region will be formed in the electron supply layer 9. From the equation (3), the thickness W of the depletion region, when the gate bias is 0 V, is: EQU W=(2.epsilon.Vb/q.multidot.Nd).sup.1/2
where Vb is 0.92 V. Thus, the thickness W is 178 .ANG.. Then, the thickness a of the electron supply layer 9 is equal to d+W, which is equal to 350 .ANG..
The doping concentration Nd and the thickness a of the electron supply layer 9 of HEMTs are 4.times.10.sup.18 cm.sup.-3 and 350 .ANG., respectively, and, accordingly, Nd.multidot.a is equal to 14.times.10.sup.12 cm.sup.-2. This value is substantially larger than the product Nd.multidot.a of ordinary GaAs MESFETs which is equal to 2.4.times.10.sup.12 cm.sup.-2. This means that the breakdown withstanding voltage VB of HEMTs is 4-5 V which is very small. Thus, by virtue of having a high saturation velocity Vs, an HEMT has a high cutoff frequency f.sub.T and an improved gain, but its maximum channel current If and breakdown withstanding voltage are small. Therefore, it is difficult to provide HEMTs with an improved power characteristic.
To sum up, the saturation velocity Vs can be improved for conventional N-type AlGaAs/GaAs HEMTs, but there is an upper limit on the free electron concentration for N-type AlGaAs, and, because of this limitation, the maximum channel current If cannot be increased and the breakdown withstanding voltage is less than one-half of that of MESFETs.